Question: The grades on a math midterm at Loyola are normally distributed with $\mu = 76$ and $\sigma = 5.5$. Gabriela earned a n $80$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{80 - {76}}{{5.5}}} $ ${ z \approx 0.73}$ The z-score is $0.73$. In other words, Gabriela's score was $0.73$ standard deviations above the mean.